In our context, [1]} proposed the fused lasso estimator \(\hat{\theta }^{FL}\)  that induces sparsity on both \(\theta \)  and \(\eta \) , defined as
\(\hat{\theta }^{FL} = \arg \min _{\theta \in \mathbb {R}^n}\left\lbrace \dfrac{1}{2}\Vert y-\theta \Vert _2^2 + \lambda _1 \Vert \theta \Vert _1 + \lambda _2\Vert \eta \Vert _1\right\rbrace ,\) 
